Oh man, I wrote a paper on this back in undergrad for one of those required English classes! I found a great source from 1868 by William Rounseville Alger called The Friendships of Women. You can read the whole thing here.

I can't say how things were before or after this work was written, but it should give a nice slice of what the situation was like in the late 19th century.

First of all, it's awfully telling that the first chapter of his book is entitled "Have Women No Friendships?" He explains that the common belief, among men as well as the women themselves, was that "feminine hearts are so complex, changeable, elusive" that friendship with them is impossible. He refutes this viewpoint immediately, but the fact that he has to devote a whole chapter of his book to refuting it should tell you a bit about how his audience felt about the matter.

He discusses various familial friendships (mother and son, father and daughter, brother and sister, husband and wife) before moving onto true "platonic love." He decries the notion, apparently prevalent at the time, that a woman and a man could not be friends without getting sexually involved. He quotes Sydney Smith as saying, "It is a great happiness to form a sincere friendship with a woman; but a friendship among persons of different sexes rarely or never takes place in this country." Alger laments the fact that, when seeing a platonic cross-sex friendship, the public's "readiness to cast coarse insinuations on them is more discreditable to our hearts than it is creditable to our morals. It implies the belief that they cannot be attached as spirits without becoming entangled as animals. It is absurd to pretend that the multiplication of virtuous friendships between the sexes would foster licentiousness. Their flourishes best in their absence. Their life element, esteem, is death to licentiousness."

He goes on to tell famous stories about women and men being friends, but you get the picture: By the 19th century, cross-sex friendships were not common by any means, though they certainly had some proponents.